engine idling rough

Last week my CFI was giving me a practice checkride. We were about 4500 msl, when I did a power off stall, during which the engine started to shake! This was at approx. 3500 rpm. The engine ran smooth at higher RPM. We headed back to the airport ASAP, We came in pretty steep, instructor wanted to keep as much altitude as possible. On final I had to pull pretty hard on throttle to get it to go to idle. We finally just turned the engine off about 25 feet off the ground because of the shaking. I restarted the engine after touch down to taxi back to the hanger. I got it started and we both smelled fuel, not wanting to damage anything else we did the walk of shame and pull the bird the last 750 ft. I took the engine cover off and started looking over things and noticed that the throttle cable Nut came loose on the right carb. This would be the point of attachment to where the cable attaches to the carb. This allowed full throttle but not idle, so the two carbs were fighting each other. This caused my shaking!! I adjusted the cables back to factory spec and re locked them together! I also changed spark plugs since I smelled fuel and was guessing we fouled them. Tonight I did a few hops down the 5900 ft runway then after being pleased with that I did a few touch and go s . Upon final approach around 3000 I had alittle vibration again! We re synced the carbs after adjusting the cable, so I'm wondering if there is something I might have missed??? It runs perfect otherwise!!

Thanks
Patrick
Series 6 - rotax 912 100 hp
trigear

Here is the technique we were taught in the Rotax training class.

Mechanical Sync:

1. Disconnnect throttle cables
2. Loosen idle stop screws untill throttle plates bottom out in bore
3. Using a feeler gage (business card thickness) screw in the idle stops until you just feel drag between the screw and tab
4. Turn in screw three (3) turns
5. Repeat to other carb
6. Set throttle handle to desired idle position and tighten cable clamps

This has set a Mechanical Sync. You can start the engine and adjust the idle speed by turning the two idle stop screws (the same amount each side), in or out.

If you are careful with the procedure, you will need only minimal (if any) adjustment when you do the vacuum sync at 3000 rpm.

I would rebuild the carbs. I just did this on my 912 ul, the viten valve was sticking in my case among other issues. If you have questions contact me i may be able to help. I ordered the rebuild kit was worth the cost because it fixed a few issues. Also i broke the throttle cable banjo bolt that holds the cable to the carb lever. I also had an issue with the new bolt from the factory, not mention the cost $20 for a dang screw.

I had this problem late last year after my Kitfox sat a couple months while I recovered from surgery. I found one of the float needles had jamed in a carb. Note how the needle assembly is cocked. Replacing the needle assembly and the float arm fixed the problem.

Another problem could be getting the float bowel on wrong.

Took the plane to a Rotax mech. on Tuesday of this week, He adjusted the carb with a vaccum gauge. Engine now runs smoother that ever before!
Thanks to all who gave input it was much appreciated!